I work as a hospital SW with adults and have now been qualified for over 20 years. Unlike some others who have posted, I do enjoy my work, although it can be very stressful, particularly the pressures due to lack of resources, mountains of paperwork and challenging relationships with Health colleagues. I second what people have said about shadowing some SWs to give you a better idea of the range of possiblities, and that's also expected as part of the course. Have you thought which area of SW might attract you? - although, of course, you may change your mind as you experience different settings.
I work part time, as do several of my colleagues, and I think it's generally quite easy to find hours to suit you, although stress levels can be greater because of the time management skills required due to having to complete pieces of work before your day off/before you leave to pick up the children from school. I do 4 days/week, 2 long and 2 short (school hours), so always have to have in my head what day of the week it is and my deadline. However, I've managed that for many years (my dd is nearly 13 and ds 9.5) and there's also the scope for things such as parental leave if a child is poorly and you've used up your allocated holiday - which is comparatively generous anyway. Thankfully mine are both generally very healthy and so that's not been a big issue. Once your children are at school the long holidays can be a challenge, particularly if several other team members have kids, and we're only allowed 3 people off at any one time - so you have to make sure you plan well in advance.
I've also taken SW students for many years, of whom several have had dependent children (and I've managed this in spite of being part time), and most have coped admirably with the demands of the placement and the academic work.
We have had part-time/job-share managers as well, which shows both equality of opportunity and demonstrates that motherhood and advancement in SW are perfectly possible.
Altogether I think it's a real privilege and humbling experience to be able to stand alongside people in their time of need, and although I'm sure it's right what some other posters have said about child protection work (which I personally wouldn't want to do anyway), we do have people who genuinely appreciate the help we give them and it is possible to make a difference in someone else's life, which is what it's all about. (I'm still quite idealistic in spite of having done it for so long!). Hope that helps.